What is the sum from n=1 to infinity of (2n)/(n^4+1) ?

The sum from n=1 to infinity of (2n)/(n^4+1) is converges

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sum from n=1 to infinity of (2n)/(n^4+1)

n = 1 \sum \infty \frac{2 n}{n ^{4} + 1}

converges

Solution steps

n = 1 \sum \infty \frac{2 n}{n ^{4} + 1}

Apply the constant multiplication rule:

\sum c \cdot a_{n} = c \cdot \sum a_{n}

= 2 \cdot n = 1 \sum \infty \frac{n}{n ^{4} + 1}

Apply Series Comparison Test:

converges

= 2 converges

= converges

What is the sum from n=1 to infinity of (2n)/(n^4+1) ?
The sum from n=1 to infinity of (2n)/(n^4+1) is converges